Before Fokas and Lenells' work, Eq.(REF ) has been solved using
direct linearization approach [1]}.
More recently,
by virtue of a clear integrable background associated with the well studied KN spectral problem,
solutions of the FL equation (REF ) or (REF ) have been derived by means of
the Riemann-Hilbert method or inverse scattering transform
[2]}, [3]}, [4]},
dressing chain [5]},
algebro-geometric method [6]},
Darboux transformation [7]}, [8]}, [9]},
and a variable separation technique [10]}.
Note that in [9]} Eq.(REF ) is shown to be related to
the Zakharov-Shabat and Ablowitz-Kaup-Newell-Segur (ZS-AKNS) spectral problem.
